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**Unformatted text preview: **pretend the y -axis is a mirror, the reﬂection of (−2, 3)
across that axis would be (2, 3). If we reﬂect across the x-axis and then the y -axis, we would go
from (−2, 3) to (−2, −3) then to (2, −3), and so we would end up at the point symmetric to (−2, 3)
about the origin. We summarize and generalize this process below.
Reﬂections
To reﬂect a point (x, y ) about the:
• x-axis, replace y with −y .
• y -axis, replace x with −x.
• origin, replace x with −x and y with −y . 1.1.1 Distance in the Plane Another important concept in geometry is the notion of length. If we are going to unite Algebra
and Geometry using the Cartesian Plane, then we need to develop an algebraic understanding of
what distance in the plane means. Suppose we have two points, P (x1 , y1 ) and Q (x2 , y2 ) , in the
plane. By the distance d between P and Q, we mean the length of the line segment joining P with
Q. (Remember, given any two distinct points in the plane, there is a unique line containing both
points.) Our goal...

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